Categorical Models for a Semantically Linear Lambda-calculus

This paper is about a categorical approach to model a very simple Semantically Linear λcalculus, namedSlλ-calculus. This is a core calculus underlying the programming language SlPCF. In particular, in this work, we introduce the notion of Slλ-Category, which is able to describe a very large class of sound models of Slλ-calculus. Slλ-Category extends in the natural way Benton, Bierman, Hyland and de Paiva’s Linear Category, in order to soundly interpret all the constructs of Slλ-calculus. This category is general enough to catch interesting models in Scott Domains and Coherence Spaces.